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Linear equationsAlgebraMiddle schoolabout 1:08

Solve 0.2(x - 5) = 0.5x + 1: animated lesson

A narrated, step-by-step linear equations video lesson with captions. Final answer: x = -20/3 ≈ -6.6666667.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.4 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Solving an equation
$0.2~\left( x-5\right) = 0.5~ x+1$
2. Steps, part 1
1. $0.2~\left( x-5\right) = 0.5~ x+1$
  Start with the equation
2. $\frac{1}{5}x - 1 = \frac{1}{2}x + 1$
  Simplify each side (distribute and combine like terms)
3. $-\frac{3}{10}x - 1 = 1$
  Subtract 1/2x from both sides
4. $-\frac{3}{10}x = 2$
  Add 1 to both sides
3. Steps, part 2
1. $x = 2 \div -\frac{3}{10} = -\frac{20}{3}$
  Divide both sides by -3/10 (multiply by its reciprocal)
4. The answer
$x = -\frac{20}{3} \approx -6.6666667$
x = -20/3 ≈ -6.6666667
5. Check
- x = -6.6666667: left side = -2.3333333, right side = -2.3333333 ✓

Transcript

The problem. Here is the problem: 0.2(x minus 5) equals 0.5x plus 1. A linear equation in x: isolate x using inverse operations.

Steps, part 1. Start with the equation. Simplify each side (distribute and combine like terms). Subtract 1 over 2x from both sides. Add 1 to both sides.

Steps, part 2. Divide both sides by negative 3 over 10 (multiply by its reciprocal).

The answer. So the answer is x equals negative 20 over 3 approximately negative 6.6666667. Doing the same operation to both sides keeps the equation balanced. Undoing addition, then multiplication, leaves x alone.

Check. x equals negative 6.6666667: left side equals negative 2.3333333, right side equals negative 2.3333333, which checks out.

About linear equations

Solve one-variable linear equations, including ones with brackets and fractions, and check the solution.

Solve 0.2(x - 5) = 0.5x + 1: Animated Step-by-Step Lesson